--- /dev/null
+ subroutine interv ( xt, lxt, x, left, mflag )
+c from * a practical guide to splines * by C. de Boor
+computes left = max( i : xt(i) .lt. xt(lxt) .and. xt(i) .le. x ) .
+c
+c****** i n p u t ******
+c xt.....a real sequence, of length lxt , assumed to be nondecreasing
+c lxt.....number of terms in the sequence xt .
+c x.....the point whose location with respect to the sequence xt is
+c to be determined.
+c
+c****** o u t p u t ******
+c left, mflag.....both integers, whose value is
+c
+c 1 -1 if x .lt. xt(1)
+c i 0 if xt(i) .le. x .lt. xt(i+1)
+c i 0 if xt(i) .lt. x .eq. xt(i+1) .eq. xt(lxt)
+c i 1 if xt(i) .lt. xt(i+1) .eq. xt(lxt) .lt. x
+c
+c In particular, mflag = 0 is the 'usual' case. mflag .ne. 0
+c indicates that x lies outside the CLOSED interval
+c xt(1) .le. y .le. xt(lxt) . The asymmetric treatment of the
+c intervals is due to the decision to make all pp functions cont-
+c inuous from the right, but, by returning mflag = 0 even if
+C x = xt(lxt), there is the option of having the computed pp function
+c continuous from the left at xt(lxt) .
+c
+c****** m e t h o d ******
+c The program is designed to be efficient in the common situation that
+c it is called repeatedly, with x taken from an increasing or decrea-
+c sing sequence. This will happen, e.g., when a pp function is to be
+c graphed. The first guess for left is therefore taken to be the val-
+c ue returned at the previous call and stored in the l o c a l varia-
+c ble ilo . A first check ascertains that ilo .lt. lxt (this is nec-
+c essary since the present call may have nothing to do with the previ-
+c ous call). Then, if xt(ilo) .le. x .lt. xt(ilo+1), we set left =
+c ilo and are done after just three comparisons.
+c Otherwise, we repeatedly double the difference istep = ihi - ilo
+c while also moving ilo and ihi in the direction of x , until
+c xt(ilo) .le. x .lt. xt(ihi) ,
+c after which we use bisection to get, in addition, ilo+1 = ihi .
+c left = ilo is then returned.
+c
+ integer left,lxt,mflag, ihi,ilo,istep,middle
+ double precision x,xt(lxt)
+ data ilo /1/
+ save ilo
+ ihi = ilo + 1
+ if (ihi .lt. lxt) go to 20
+ if (x .ge. xt(lxt)) go to 110
+ if (lxt .le. 1) go to 90
+ ilo = lxt - 1
+ ihi = lxt
+c
+ 20 if (x .ge. xt(ihi)) go to 40
+ if (x .ge. xt(ilo)) go to 100
+c
+c **** now x .lt. xt(ilo) . decrease ilo to capture x .
+ istep = 1
+ 31 ihi = ilo
+ ilo = ihi - istep
+ if (ilo .le. 1) go to 35
+ if (x .ge. xt(ilo)) go to 50
+ istep = istep*2
+ go to 31
+ 35 ilo = 1
+ if (x .lt. xt(1)) go to 90
+ go to 50
+c **** now x .ge. xt(ihi) . increase ihi to capture x .
+ 40 istep = 1
+ 41 ilo = ihi
+ ihi = ilo + istep
+ if (ihi .ge. lxt) go to 45
+ if (x .lt. xt(ihi)) go to 50
+ istep = istep*2
+ go to 41
+ 45 if (x .ge. xt(lxt)) go to 110
+ ihi = lxt
+c
+c **** now xt(ilo) .le. x .lt. xt(ihi) . narrow the interval.
+ 50 middle = (ilo + ihi)/2
+ if (middle .eq. ilo) go to 100
+c note. it is assumed that middle = ilo in case ihi = ilo+1 .
+ if (x .lt. xt(middle)) go to 53
+ ilo = middle
+ go to 50
+ 53 ihi = middle
+ go to 50
+c**** set output and return.
+ 90 mflag = -1
+ left = 1
+ return
+ 100 mflag = 0
+ left = ilo
+ return
+ 110 mflag = 1
+ if (x .eq. xt(lxt)) mflag = 0
+ left = lxt
+ 111 if (left .eq. 1) return
+ left = left - 1
+ if (xt(left) .lt. xt(lxt)) return
+ go to 111
+ end
projects / mothur.git / blobdiff